 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| A.A. Zevin and L.A. Filonenko, "The stability of the parametric oscillations of second-order non-linear systems," J. Appl. Math. Mech. 76 (1), 48-55 (2012) |
| Year |
2012 |
Volume |
76 |
Issue |
1 |
Pages |
48-55 |
| Title |
The stability of the parametric oscillations of second-order non-linear systems |
| Author(s) |
A.A. Zevin (Dnepropetrovsk, Ukraine, zevin@westa-inter.com)
L.A. Filonenko (Dnepropetrovsk, Ukraine) |
| Abstract |
The parametric oscillations of strongly non-linear systems with one degree of freedom are considered using a more general definition of these oscillations than the generally accepted definition. Stability criteria, that are verifiable using the signs of the derivatives of the amplitude-frequency characteristics, are found for the two families of periodic solutions corresponding to the fundamental parametric resonance. A condition is indicated under which the latter are monotonic and, as a result, one of the families is stable and the other is unstable. It is shown that, in a system with a concave non-monotonic elastic characteristic, the stable family loses stability for fairly large amplitudes and this effect is not revealed by the well-known analytical methods of non-linear mechanics. |
| Received |
18 May 2011 |
| Link to Fulltext |
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